Uniqueness of non-commutative divergence cocycle (in French)

19.06.2025 13:15 – 14:00

We show that, for n ≥ 3, 1-cocycles of degree zero on the Lie algebra of derivations of the free associative algebra T (A_n) with values in |T (A_n)| ⊗ |T (A_n)| are linear combinations of the non-commutative divergence and its switch, when restricted to finite-degree quotients. Here, |T (A_n)| denotes the space of cyclic words. Furthermore, we study 1-cocycles of degree zero on the Lie algebra of symplectic derivations of the free Lie algebra L_2n, and prove the uniqueness of the Enomoto–Satoh trace.

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Conseil Général 7-9, Room 1-15

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